Numerical simulation of autoclaved aerated concrete masonry wall subjected to close-in explosion and the structural damage assessment

In this study, we investigated the destructive effect of autoclaved aerated concrete (AAC) masonry walls subjected to close-in explosions. First, full-size refined finite-element models of the AAC masonry wall were established, and the accuracy of the models was verified by comparison with the test results. The destruction pattern and damage characteristics of the AAC wall were studied, and the effects of block size, wall thickness, mortar compressive strength, and explosion distance on the destruction degree of the AAC masonry walls were analyzed. The results showed that the destruction pattern of the AAC masonry wall subjected to close-in explosion manifested as punching damage in the middle of the wall. When the scaled distance remained unchanged, the punching damage area of the AAC masonry wall was positively correlated with the block size and negatively correlated with the wall thickness and mortar compressive strength. When the explosive equivalent remained unchanged and the explosion distance increased, the punching damage area first increased and then decreased. According to the damage mechanism of the AAC masonry wall, a calculation method for predicting the punching damage area of the AAC masonry wall was established, and the accuracy of this method was verified by comparing it with the numerical results. In addition, the damage criterion based on the punching damage area was established to determine the destruction levels of AAC masonry walls.


Numerical model verification
Due to fast propagation speed, high peak pressure, and short-duration characteristics, the dynamic response and failure modes of AAC masonry blocks will significantly differ from those under static load.Yu et al. 32 conducted dynamic response and damage tests of an AAC masonry wall under explosion load, where during the test, 3000 kg of TNT charge was placed 70 m in front of the AAC masonry wall.The AAC masonry wall specimens with dimensions of 3.6 × 3.6 × 0.2 m, and the experimental setup, are shown in Fig. 1.The basic mechanical parameters of the AAC were as follows: the uniaxial compressive strength was 3.5 × 10 6 Pa, Young's modulus was 5.3 × 10 8 Pa, the Poisson's ratio was 0.2, the mean density was 500 kg/m 3 , and the dimensions of the block were 0.6 × 0.6 × 0.2 m.The mortar had a compressive strength of 7.6 × 10 6 Pa.Subsequently, the dynamic response and damage of the AAC masonry wall under explosion load were simulated to verify the reliability and accuracy of the numerical model.

Finite element model
The numerical model of the AAC masonry wall was divided into a separation model and a homogenization model.The separation model was established by treating the block and mortar separately, to accurately simulate the bonding slip and failure processes between the blocks and mortar.Due to the small difference in mechanical properties between the AAC and mortar, the contact surface with zero-thickness could be applied to replace the mortar.In this section, a separation model of the AAC masonry wall was developed using commercial finite element software LS-DYNA, as shown in Fig. 2. The AAC block and external frame adopted the Lagrangian calculation method, in which the coordinates moved with the material, where all node displacement and rotation of the concrete frame were fixed.

Material model
The material model *Mat_96 (MAT_BRITITLE_DAMAGE) was employed to model the AAC blocks.This model consisted of an anisotropic brittle damage model, which could be applied to a wide variety of brittle materials.According to the GB/T11971-1997 test standard 34 , Li et al. 30 poured 0.1 m AAC cube specimens and used an MTS servo-hydraulic testing machine to assess the mechanical properties of the AAC specimen and determine the material model parameters of the AAC block.The tensile strength, shear strength, fracture energy, and shear retention factor were obtained from Ref. 30 , while the density, compressive yield strength, modulus of elasticity, and Poisson's ratio were obtained from Ref. 32 .The detailed model parameter values are listed in Table 1.To accurately simulate AAC masonry wall failure under explosion load and prevent the excessive distortion of elements, erosion criteria were used to simulate the failure of materials.The maximum principal strain was used as the failure criterion, and the value was defined as 0.01.Of note, the value of failure strain lacked a relevant theoretical basis, which was determined mainly by trial calculations in this study.

Method of load application
The fluid-solid coupling method and CONWEP method have been commonly used to apply explosion load.The fluid-solid coupling method could establish the air domain and calculate the propagation process of the explosion shock wave in air.The CONWEP method simplified these processes, which effectively reduced the complexity of the finite element model and improved the calculation efficiency.Therefore, the CONWEP method was employed to apply explosion loads with different TNT mass values and different explosion distances to the AAC masonry wall.
CONWEP, an explosion load calculation method developed on the basis of fitting a large number of experimental data 35 , was built using the LS-DYNA program, and the explosion load was applied to the selected surface by combining the *LOAD_BLAST_ENHANCED and *LOAD_BLAST_SEGMENT keywords.The overpressure time curve could be represented by adopting the modified Friedlander equation, according to where P S0 is the peak incident overpressure, t 0 is the positive phase duration, and b is the decay attenuation coefficient of the waveform.The peak overpressure on the structure was also related to the incident angle θ.The CONWEP method could generate the equivalent overpressure value, as expressed by where P ref is the reflected pressure and P in is the incident pressure, which could be calculated by Eq. ( 1).

Contact surface
The bonding between the AAC blocks as well as between the AAC wall and external frame was simulated as tie-break contacts in the numerical model, to accurately describe separation and sliding between the contact surfaces.Contact was achieved using the *TIEBREAK_SURFACE_TO_ SURFACE command in LS-DYNA 36 .This contact was governed by the stress-based failure criterion, according to where f n and f s denote the normal stress and shear stress on the contact surface, respectively, and F n and F s are the normal failure stress and shear failure stress, respectively, which could be characterized by the tensile strength and shear strength of the mortar.When the stress state on the contact surface satisfied Eq. ( 3), mutual contact movement between the blocks would be constrained by friction.In this study, the static and dynamic coefficients of friction factor were 0.4 and 0.3, respectively, while the normal failure stress F n and shear failure stress F s were 3 × 10 5 Pa.The above parameters were obtained from the trial calculation and validated by the experimental data.

Mesh size
In the numerical simulations, which simulated interactions between the explosion load and masonry wall, the accuracy of the numerical results depended significantly on the mesh size of the finite element model.To ensure the accuracy of the numerical results, convergence analysis of the finite element model mesh size was carried out to determine the appropriate parameters in this section.
Three finite element models of the AAC masonry wall were built with mesh sizes of 0.01, 0.02, and 0.05 m to simulate interactions between the explosion load and the AAC masonry wall.Figure 3 illustrates the final damage of the finite element models with different mesh sizes when the explosive equivalent was 1 kg and the explosion distance was 0.5 m.With a decrease in mesh size, the final damage of the AAC masonry wall tended to converge.However, we observed that the finer the solid mesh, the more accurate the calculation of the final AAC masonry wall damage.Considering the calculation accuracy and computational efficiency, a mesh size of 20 mm was chosen, and the finite element model had a total of 280,000 solid elements, 353,265 nodes, and 1,485,000 degrees of freedom.

Comparison of the experimental and numerical results
The final damage of the AAC masonry wall in the test is shown in Fig. 3.The surfaces of certain blocks in the margin of the AAC masonry wall developed fragmentation and peeling, and a 1.2 × 1.2 m square hole developed (1) in the center portion of the AAC masonry wall.Relatively intact AAC blocks fell off the front and back of the wall, which was mainly caused by the destruction of the cement mortar.Figure 4 shows the final damage of the AAC masonry wall in the numerical calculation.Due to the failure of elements and the displacement of the blocks after the failure of the contact surface, a 1.3 × 1.2 m rectangular hole developed in the center portion of the wall.
The failure mode and damage area of the AAC masonry wall in the numerical calculation essentially agreed with the experimental results, which verified the accuracy of the numerical model and the material parameters.

Dynamic response of the AAC masonry wall under close-in explosion
In this section, the dynamic response and damage failure of the AAC masonry wall under close-in explosion load were numerically simulated.Based on the simulation results, the dynamic response characteristics and damage failure modes of the AAC masonry wall under close-in explosion load were analyzed.Moreover, the influence of parameters such as the block size, wall thickness, mortar compressive strength, and explosion standoff distance on the dynamic response and damage of the AAC masonry wall under close-in explosion was assessed.

Typical simulation results
An AAC masonry wall with a width of 3.  the tensile stress wave.At t = 0.05 ms, damage to the AAC masonry wall was further aggravated, and the stress of the contact surface between certain blocks in the margin portion exceeded the shear limit, causing the movement of blocks away from the wall.At t = 0.2 s, the punching failure portion of the AAC masonry wall further expanded, and a rectangular hole formed in the middle portion of the wall due to damage and slip of the blocks.
According to the numerical results, the contact surface between the blocks was the vulnerable portion under close-in explosion load, which was prone to damage, and wall damage occurred in the form of punching failure.

Parameter study
The AAC masonry wall was composed of blocks and mortar, and the explosion resistance of the wall was affected by the sizes of the blocks and the mechanical properties of the mortar.In addition, for the same mass of TNT charge, the pressure distribution on the surface of the wall varied with a change in explosion distance.In this section, the effects of block sizes, wall thickness, mortar compressive strength, and explosion distance on the dynamic response and damage degree of the AAC masonry wall under close-in explosion were discussed.

Effect of block size
To explore the differences in AAC masonry wall explosion resistance with different block sizes, six finite element models with different block sizes were constructed.The mesh size and material parameters were consistent with Section "Dynamic response of the AAC masonry wall under close-in explosion".In the calculation examples, the distances from the TNT charge to the center of the wall were all 0.5 m, and the explosive equivalent was 1 kg.Table 2 shows the peeling area and punching hole area of the AAC masonry wall.When the number of masonry blocks was increased from 60 to 255, the peeling failure area of the front explosion wall surface decreased by 20.7%, and the punching hole area decreased by 8.8%.The reason was that when the dimensions of the wall were the same and the size of the blocks decreased, the amount of mortar used for masonry bonding increased, and the explosion energy absorbed by the mortar also increased.Due to the higher strength of the mortar than the blocks, the damage degree of the AAC masonry wall was reduced.
Figure 6 shows the final damage to the AAC walls with different block sizes under close-in explosion, revealing that the peeling area and punching hole of the AAC wall were almost symmetrically distributed around the center of the wall.When the length of the block was constant, the transverse size of the punching hole was the same, and the lateral size was an integer multiple of the block height.When the height of the block was constant, the lateral size of the punching hole was the same, and the transverse size of the punching hole in the masonry wall with a small block size and identical length and height was an integer multiple of the block length.In addition, the transverse size of the punching hole for the masonry wall with a large block size and aspect ratio greater than one was a half-integer multiple of the block length.The reason for this phenomenon was that when the block size was small with a larger lateral stiffness and longitudinal stiffness, the blocks were not prone to punching failure.When the height of the blocks was small and the length was large, the lateral stiffness was lower than the longitudinal stiffness, and shear failure would occur in the middle of the blocks.As the vulnerable portion of the AAC masonry wall, the bonding layer between the blocks was damaged first under close-in explosion load, which caused the movement of the blocks.Therefore, the lateral size of the AAC masonry wall punching hole was an integer multiple or half-integer multiple of the length of the blocks, and the longitudinal size was an integer multiple of the block height.
In summary, with a decrease in block size, the shear resistance effect of the block increased, and the area of the punching hole of the AAC masonry wall decreased, while the shape of the punching hole changed from a rectangle to an approximate circle.However, the numerical results also showed that the decrease in block size had a limited effect on the improved explosion resistance of the AAC masonry wall.

Effect of the wall thickness
The dynamic responses and damage effects of the AAC masonry walls with different thicknesses under the same explosion differed.To explore the influence of thickness on the AAC masonry wall dynamic response and damage effect under explosion load, five numerical models of the AAC masonry wall were built with thicknesses of 100, 150, 200, 250, and 300 mm.The grid division and material parameters were consistent with Section "Numerical model verification".The distances from the TNT charge and wall were 0.5 and 2.0 m, respectively, and the explosive equivalent was 1 kg.
Table 3 summarizes the final damage condition of the AAC masonry wall with different thicknesses.When the explosion distance was 0.5 m, punching failure occurred in the AAC masonry walls with different thicknesses.With an increase in wall thickness from 0.1 to 0.3 m, the punching hole area decreased by 90.6%.When the explosion distance was 2.0 m, the middle area of the masonry wall with a thickness of 0.1 m was slightly damaged, and the dynamic response of the other walls was within the elastic range.With an increase in wall thickness from 0.1 to 0.3 m, the maximum displacement of the wall decreased by 99.6%.The reason for this phenomenon was that with an increase in wall thickness, the sectional inertial moment parallel to the direction of explosion loading and bonding force between the mortar and blocks increased.Therefore, the shear capacity of the masonry wall significantly improved, which enhanced its explosion resistance.
Figure 7 shows the final damage condition of masonry walls with different thicknesses when the explosion distance was 0.5 m, with B denoting the thickness of the masonry wall.When the thickness of the wall was 0.10 m,  the blocks in the middle area of the masonry wall were crushed because the pressure exceeded the strength of the material, and the surrounding area was ejected from the frame in an integral form, and the punching failure area was approximately circular.When the wall thickness was increased to 0.15 m, the punching failure area was relatively reduced, and its shape remained approximately circular.With a further increase in wall thickness, only slight peeling damage occurred in the surrounding area of the masonry wall.The range of crushed blocks in the middle area of the masonry wall gradually decreased, and the shape of the punching hole changed from circular to square.The reason for this phenomenon was that when the wall thickness was small, the shear resistance of the masonry wall was low, and the block was prone to punching failure with a shape distribution of the explosion load.Therefore, the punching hole was approximately circular.With an increase in thickness, the sectional shear resistance of the masonry wall was enhanced, and the middle of the block and contact surfaces between the block and mortar were vulnerable.As a result, shear failure occurred when the explosion loading was high.Therefore, the punching hole was approximately square.

Effect of mortar compressive strength
The compressive strength of the mortar served as a key factor that influenced the explosion resistance of the AAC masonry wall.To analyze the influence of mortar compressive strength on the damage degree of the wall under close-in explosion, four numerical AAC masonry wall models were built with mortar compressive strengths of 2.5, 5, 7.5 and 10 MPa.The TNT explosion quantity was 1 kg, and the explosion distances were 0.5 and 0.2 m, where the corresponding scaled distances were 0.5 and 2 m/kg 1/3 .In this section, mortar with different compressive strengths was obtained by changing the normal failure stress and shear failure stress values in the TIEBREAK contact.Equations ( 4) and ( 5) present the calculation methods of the average tensile strength σ t and average shear strength σ v of the brick masonry along the straight joint, according to Chinese code GB55007-2021 34 : (4) σ t = 0.125 f c , where f c is the compressive strength of mortar.Figure 8 shows the final damage of the AAC masonry wall with different mortar compressive strengths when the scaled distance was 0.5 m/kg 1/3 .When the compressive strength was 2.5 × 10 6 Pa, partial bonding between the wall and frame was damaged, and the margin portion of the front and back explosion surfaces of the wall developed serious peeling.In addition, a punching hole appeared in the middle area of the wall.When the compressive strength was 5.0 × 10 6 Pa, no failure cracks appeared at the bonds between the wall and the frame.The peeling areas of the front and back explosion surfaces of the wall decreased by 12.1%, and the punching hole area was reduced by 23.0%.When the compressive strength was increased to 1.0 × 10 7 Pa, the peeling areas of the front and back wall explosion surfaces decreased by 46.4%; thus, the punching hole area was reduced by 65.5%.This indicated that the damage degree of the AAC masonry wall decreased with an increase in mortar compressive strength.
Figure 9 shows a comparison between the different mortar compressive strengths of the center displacements and velocity time history curves of the AAC masonry wall when the scaled distance was 2 m/kg 1/3 .Under this explosion load, the dynamic response of the AAC masonry wall was in the elastic range.With an increase in mortar compressive strength, the displacement and velocity peak of the wall center gradually decreased, and the vibration frequency gradually increased, while the time for the wall to return to the static range gradually decreased.
The above analysis showed that with an increase in the compressive strength of the mortar, the bonding surface strength between the block and mortar increased, which induced an increase in the integrity of the AAC masonry wall and enhanced the dissipation effect of the wall on the explosion energy.The maximum displacement and damage degree of the masonry wall tended to decrease.Therefore, enhancing the compressive strength of the mortar allowed the wall to improve the structural resistance to explosion damage.

Effect of explosion distance
With the same explosive equivalent, the pressure and impulse distribution on the surface of the wall changed with a variation in explosion distance.To investigate the influence of explosion distance on the damage degree of the AAC masonry wall, nine different explosion distance numerical models were built, and the explosive quantity was 2 kg.Table 4 summarizes the final damage condition of the AAC masonry walls with different explosion distances.With an increase in explosion distance, the punching hole area of the wall first increased and then decreased.In these calculation examples, the damaged area was concentrated in the middle portion of the masonry wall.With an increase in explosion distance, the punching failure area first increased and then  decreased.When the ratio of explosion distance to charge radius exceeded 30, the explosion loading on the wall surface significantly decreased, which was less than the bonding force between the mortar and the blocks.
Only the central area slightly exceeded the compressive strength of the AAC, which caused minor peeling on the surface of a few blocks.Therefore, with an increase in the explosion distance, the failure mode of the AAC masonry wall changed from severe punching failure to minor peeling failure.
Figure 10 shows the final damage of the AAC masonry walls when the explosion distances were 0.5, 0.8, and 1.5 m.When the explosion distance was 0.5 m, a large number of fragments were generated due to the high explosion load in the middle portion of the wall, which exceeded the compressive strength of the block.The weak explosion load in the margin portion of the wall did not cause the destruction of the blocks; however, some blocks were displaced due to the failure of the contact surfaces, thus forming a punching hole.When the explosion distance was increased to 0.8 m, the explosion load in the middle portion of the wall was relatively reduced and the number of fragments relatively decreased.However, the number of blocks that fell off the wall increased, which caused an increase in the area of the punching hole.When the explosion distance was further increased to 1.5 m, few fragments were observed in the middle area of the wall, and the area of blocks that fell off the wall was relatively reduced, which led to a decrease in the area of the punching hole.The reason for this phenomenon was that when the explosion distance was small, the energy generated by the explosion mainly acted on the middle area of the wall.The material strength of the blocks played a major role in resisting the explosion, and the bond strength between the blocks played a minor role.As the explosion distance increased, the explosion energy acting on the wall gradually decreased, and the explosion load distributed on the wall became more homogeneous.The proportion of explosion energy dissipated by the material strength of the blocks gradually decreased, and the proportion of explosion energy dissipated by the bonding strength between the blocks gradually increased.Therefore, the area of compressed blocks gradually decreased, and the range of blocks that fell off the wall gradually increased, which caused an increase in the punching hole area of the wall.With a further increase in the explosion, the bonding strength between the blocks played a main role in resisting the explosion load.Due to the reduced explosion energy on the wall, the range of blocks that fell off the wall gradually decreased, and the punching hole area of the AAC masonry wall decreased.
Figure 11 shows the distribution of the peak value of shock wave reflection overpressure along the wall height under the above three conditions.The results revealed that the overpressure in the middle area of the wall gradually decreased with an increase in explosion distance, and the load concentration of the wall gradually increased, which caused a load range expansion of the contact surface between the blocks.Therefore, the area of blocks that fell off the wall increased.With a further increase in explosion distance, the explosion load on the wall decreased and showed a more uniform distribution.The explosion load range that caused the failure of the contact surface between blocks was reduced, and the damage degree of the wall decreased.This further showed that when the explosive equivalent was constant, the damage degree of the AAC masonry wall first increased and then decreased with an increase in explosion distances.

Damage assessment
The reasonable definition of failure criterion is an important prerequisite for the evaluation of damage degree of the structural members.Commonly used failure criteria of masonry walls involve scaled distance, the ultimate displacement of the wall, and the rotation angle of the support.However, these failure criteria can only assess whether the masonry wall will be damaged and cannot assess the damage degree of the masonry wall.In this section, we proposed a damage criterion based on the punching failure area of the wall, which was used to assess the damage degree of the masonry wall under close-in explosion load.The damage mechanism of masonry walls under close-in explosion load was different from that of a homogeneous structure.To analyze the punching hole area of the masonry wall under close-in explosion load, the following assumptions were proposed.(1) The explosive was placed in front of the center of the front surface of the wall to ensure that the incident angle was zero degrees when the explosion shock wave propagated and impacted the front surface of the wall.(2) The time when the explosion shock wave reached each point of the wall was neglected.
(3) Friction between the mortar and blocks was neglected.
As previously mentioned, the transverse size of the punching hole of the masonry wall under close-in explosion load was the integer multiple or half-integer multiple of the length of the block, and the longitudinal size consisted of an integer multiple of the block height.To simplify this analysis, a zero-thickness bonding surface was inserted in the middle of the block to transform a complete block into two half-blocks, as shown in Fig. 12.
Due to the load and structure symmetry, the 1/4 structure was analyzed.Under close-in explosion load, the blocks in the middle area of the masonry wall were crushed due to high pressure, and the blocks in the margin area fell off the wall due to failure of the bonding surface between the mortar and blocks.Therefore, the punching hole area of the masonry wall was mainly determined by the bond strength between the mortar and blocks.A coordinate system was established with the center of the masonry wall as the origin, and the blocks were numbered and analyzed, as shown in Fig. 13.The bonding force I and explosion load F of the block were determined by where σ t is the bonding strength between mortar and block, S c is the contact surface between the mortar and block, l, b, and h denote the length, width, and height of the block, respectively, and S p is the front explosion surface.When the explosive load of the block exceeded the bonding force, the blocks fell off the wall.For a given set of working conditions, the following data were obtained: m (block rows), n (block columns), l 0 (block length), b 0 (block width), h 0 (block height), σ t0 (bonding strength), and P 0 (explosion load).We then substituted l 0 , b 0 , h 0 , and σ t0 into Eq.( 6) to obtain I 0 and substituted P 0 into Eq.( 7) to acquire F 0 .The process of determining the corner block B edge at the punching hole was as follows: (1) If I mn < F mn , the block B mn was located at the corner of the punching hole.Assuming that the horizontal distance from the upper right corner of B edge to the center of the wall was L and the longitudinal distance was H, the punching hole area S of the masonry wall could be obtained by Table 5 shows a comparison between the numerical and calculation results of the punching hole area of the masonry wall in Section "Dynamic response of the AAC masonry wall under close-in explosion", indicating that most of the calculation results were higher than the numerical results.This was because friction between the bond surface, mortar, and blocks was neglected in this assumption, and the constraint force of the block in the calculation model was less than the actual constrained force.As a result, the calculated punching failure area was higher than the numerical results.The error between the numerical results and calculation results did not exceed 15%, which met the actual engineering requirements.Therefore, the calculation method of the punching hole area of the masonry wall proposed in this section is effective.

Calculation method of punching failure area of masonry wall
According to the numerical results, the damage of AAC masonry wall could be divided into the following degrees: (a) low damage, where slight peeling damage occurred on the front and backs of the wall, and no blocks fell off the wall; (b) moderate damage, where serious peeling damage occurred on the front and backs of the wall, and   According to the numerical results, an empirical damage criterion for AAC masonry walls under close-in explosion could be obtained.The damage parameter D could be defined as where S w is the perforation of the punching hole area, and S w is the area of the wall surface.When 0 < D ≤ 0.2, the wall experienced low damage; when 0.2 < D ≤ 0.5, the wall experienced moderate damage; when 0.5 < D ≤ 0.8, the wall experienced high damage; when 0.8 < D ≤ 1, the wall experienced collapse damage.The final failure conditions of the AAC masonry walls with different damage degrees are shown in Fig. 14.

Conclusions
In this study, we investigated the dynamic response process and failure characteristics of AAC masonry walls under the action of explosion loading.A full-size three-dimensional finite element model of AAC masonry wall was constructed, and the accuracy of the numerical model was verified by comparison with previous experimental results.In this study, the failure process and mode of the AAC masonry wall were analyzed.The effects of different block sizes, wall thicknesses, mortar compressive strengths, and explosion distances on the damage degree of the AAC masonry wall were discussed.According to the analytical results, key conclusions could be drawn, as follows.
(1) The failure mode and damage degree of the AAC masonry wall numerical model were consistent with the experimental results, indicating that the proposed numerical method could accurately simulate the dynamic response and damage behavior of AAC masonry walls under explosion loading.The AAC masonry wall exhibited local punching damage under close-in explosion.
(2) With a decrease in block size, the damage degree of the AAC masonry wall was reduced, and the horizontal stiffness of the block was more significant than the vertical stiffness.However, the effects of block size on the explosion resistance performance of AAC masonry walls were very limited.(3) With an increase in wall thickness, the moment of inertia of the section parallel to the explosion load direction and bonding force between the mortar and blocks increased, the shear resistance of the masonry wall significantly increased, the area of the punching hole relatively decreased, while the shape of the punching hole changed from circular to square.Increasing the wall thickness allowed the wall to reduce the damage degree of the AAC masonry wall under close-in explosion.(4) With an increase in mortar compressive strength, the bonding strength between the mortar and blocks increased, causing an improvement in the integrity of the AAC masonry wall and an increase in the dissipation effect of the wall on the explosion energy, as well as a decrease in the maximum displacement and damage degree of the AAC masonry.Enhancing the compressive strength of mortar allowed the wall to improve structural resistance to explosion damage.(5) When the explosive equivalent remained unchanged and the explosion distance increased, the dissipation subject of explosion energy transformed from the material strength of the block to the bonding strength between the mortar and blocks, where the damage degree of the AAC masonry walls first increased and then decreased.Therefore, the combined effects of explosive equivalent and explosion distance need to be fully considered when assessing the damage degree of AAC masonry walls.(6) A method for calculating the punching hole area of masonry walls under close-in explosion load was established, and the effectiveness of the method was verified by comparison with the numerical results.A damage criterion based on the punching hole area of the AAC masonry wall was proposed to assess the damage degree of the wall under close-in explosion load.This method could provide a theoretical basis for the study of explosive energy dissipation by AAC masonry walls in the future.

Figure 3 .
Figure 3.The final damage determined by finite element models with different mesh sizes.

Figure 5 .
Figure 5. (a) Displaced cloud of the AAC masonry wall when t = 0.01 s; (b) displaced cloud of the AAC masonry wall when t = 0.05 s; (c) displaced cloud of the AAC masonry wall when t = 0.2 s.

Figure 6 .Table 3 .
Figure 6.(a) Final damage of the AAC wall with a block size of 0.60 × 0.20 × 0.20 m; (b) final damage of the AAC wall with a block size of 0.60 × 0.30 × 0.20 m; (c) final damage of the AAC wall with a block size of 0.60 × 0.15 × 0.20 m; (d) final damage of the AAC wall with a block size of 0.40 × 0.20 × 0.20 m; (e) final damage of the AAC wall with a block size of 0.20 × 0.20 × 0.20 m.

Figure 7 .
Figure 7. (a) Final damage of the AAC wall with a thickness of 0.10 m; (b) final damage of the AAC wall with a thickness of 0.15 m; (c) final damage of the AAC wall with a thickness of 0.20 m; (d) final damage of the AAC wall with a thickness of 0.25 m; (e) final damage of the AAC wall with a thickness of 0.30 m.

Figure 10 .
Figure 10.(a) Final damage of the AAC masonry wall when the explosion distance was 0.5 m; (b) final damage of the AAC masonry wall when the explosion distance was 0.8 m; (c) final damage of the AAC masonry wall when the explosion distance was 1.5 m.

Figure 11 .
Figure 11.Distribution of peak value of the reflected overpressure along the height of the wall with different explosion distances.

Figure 12 .
Figure 12. Analysis model of the masonry wall.

( 2 )
If I mn ≥ F mn , the relationship between I m−1n−1 and F m−1n−1 of block B m−1n−1 had to be compared.(3) If I m−1n−1 < F m−1n−1 , the relationships between I mn−1 and F mn−1 of block B mn−1 and between I m−1n and F m−1n of block B m−1n had to be compared.If I mn−1 < F mn−1 , I m−1n ≥ F m−1n , then block B mn−1 was located at the corner of the punching hole.If I mn−1 ≥ F mn−1 , I m−1n < F m−1n , then block B m−1n was located at the corner of the punching hole.If I mn−1 ≥ F mn−1 , I m−1n ≥ F m−1n , then block B m−1n−1 was located at the corner of the punching hole.(4) If I m−1n−1 ≥ F m−1n−1 , the relationship between I m−2n−2 and F m−2n−2 of block B m−1n−1 was compared, until the block at the corner of the punching hole was determined.

Figure 13 .
Figure 13.The punching failure analysis model of the masonry wall.

Table 1 .
Material parameters for the AAC blocks.

Table 2 .
Damage to the AAC walls with different block sizes under close-in explosion.

Table 4 .
Damage degree condition of the AAC masonry wall with different explosion distances.

Table 5 .
Comparison of numerical results and calculation results of punching failure area of AAC masonry wall.few relatively intact blocks fell off the wall; (c) high damage, where large number of blocks fell off the wall; (d) collapse damage, where the wall completely disintegrated and collapsed.